In April, the EU justice commissioner, Viviane Reding, warned that crossborder pursuits of bicycle thieves, piglet rustlers and those accused of trivial offences was damaging the authority of the European arrest warrant (EAW).

This week it was the turn of MEPs to voice their alarm – or appreciation – of the accelerated system of extradition that is meant to speed up the wheels of justice across the EU. Inevitably, questions about Julian Assange's fate resurfaced.

The EU Commission has tried to sugar the pill, promising legislation to ensure that no one facing criminal charges in any member country will be denied access to a lawyer.

"The law would require every person facing extradition under Europe's fast-track extradition regime – the EAW – to be guaranteed access to a lawyer in both countries, to ensure protection of their fundamental rights," a soothing statement from Brussels declared.

The new measure includes a "right for non-nationals to have their own country informed that they have been arrested", which, unless individuals wish to boast about bad behaviour, may sound less reassuring than intended.

Improved access to lawyers has been welcomed by Jago Russell, chief executive of Fair Trials International. He said: "It is a shocking fact that, even within Europe, people are still being denied private access to a lawyer at crucial points in their case. This law will be an important step in the right direction, towards a Europe where countries can work together to tackle serious crime, safe in the knowledge that basic defence rights will be respected."

There have been calls for the introduction of a threshold below which extradition would not be permitted for minor allegations. Poland, in particular, has become notorious among EU states for the large quantity of its warrants.

EAWs have been sought for such offences as bicycle theft, possession of 0.45 grams of cannabis, removing car tyres and stealing piglets. More than 2,400 requests were received by the UK from Poland last year.

The debate in the European parliament on Wednesday, which was launched on the initiative of the Greens, raised concerns about flaws in the EAW system. Some fear it will be expanded to provide for the extradition of those merely wanted for questioning abroad.

Catherine Heard, head of policy at Fair Trials International said: "MEPs from a broad political base clearly share our concerns about the serious and continuing misuse of the arrest warrant. Only by working together to introduce key safeguards in the European arrest warrant system will the EU produce a fairer extradition system."

Questions tabled by MEPs included the use of warrants for questioning only; warrants being issued to prosecute minor offences; countries not respecting other states' decisions to refuse extradition, leading to people being arrested repeatedly; inadequate legal representation and poor prison conditions for extradited people held in pre-trial detention.

Labour MEP, Claude Moraes and Liberal Democrat MEP, Baroness Ludford asked: "How is the commission going to guarantee that disproportionate use of the EAW is put to an immediate end both in law and practice?"

The reputation of the EAW, they warned, has been tarnished by reports of it being used for questioning instead of prosecution and execution of sentences and minor offences without proper consideration of whether surrender is proportionate. Each warrant is said to cost on average €25,000 (£22,000).

UKIP MEP Gerard Batten asked a more provocative question, inquiring whether "the case against Mr Julian Assange demonstrates the possible abuse of the EAW for political purposes"?